Question

Five circles are placed in a
rectangle as shown. If the
length of the shorter side of
the rectangle is 1, find the
length of the other side.​

Answer 1

Answer:

The length of the other side of the rectangle is 2.2units.

Step-by-step explanation:

Given that, five circles are placed in a rectangle.

The length of the shorter side of the rectangle is 1.​

As the big circle totally inscribed in the rectangle, the length of the shorter side of the rectangle is equal to the diameter of the big circle.

So, the diameter of big circle is 1 unit.

Since, there are two circles, the total length by the two big circles together is 2units.

Now coming to the two medium circles and a small circle placed at the center, the medium circles are of same size and placed symmetrically on either side of the small circle.

The center of the smaller circle is exactly at the half length of the side of the rectangle.

Thus the diameter of the medium circle and radius of small circle is 0.5unit.

Dividing symmetrically, the length of medium circle and small circle  should be 0.4 and 0.2 units respectively.

If we add it makes $0.4+0.2+0.4=1unit$, the diameter of the big circle.

Hence, the length of the other side of the rectangle is the sum of diameters of two big circles and the small circle, i.e., $1+1+0.2=2.2units$